0V on the DC/DC output. The exact same problematic behavior as with the first circuit, only this time I had not messed with it at all. After some further investigation it seemed like the MOSFETs were not connecting the cell to the rest of the circuit.
It is not clear to me if the over/discharge protection IC is failing at engaging the MOSFETs, or if the MOSFETs used for this circuit don't have the right specifications. Maybe there is some kind of gate capacitance that builds up and needs to be discharged prior to initialization of the protection circuit.
The circuit will work if either the MOSFET gates are briefly connected to B-, or if the P-/P+ terminals are connected to a solid 5V DC source, like a USB outlet.
I called browndoggadgets.com and they were able to reproduce the same (mis)behavior and graciously offered to replace my purchases with substitute circuits that should get the job done.
That means more cool stuff coming in the mail for me this week!